Question 142
Find all pairs of real numbers $(x, y)$ such that
$$
\begin{cases} \sqrt{x^2 - 2x + y^2 + 4y + 5} + \sqrt{x^2 - 8x + y^2 - 4y + 20} = 5 \\ 16x^2 + 9y^2 = 68. \end{cases}
$$
$$
\begin{cases} \sqrt{x^2 - 2x + y^2 + 4y + 5} + \sqrt{x^2 - 8x + y^2 - 4y + 20} = 5 \\ 16x^2 + 9y^2 = 68. \end{cases}
$$